Helly type problems in convexity spaces

Andreas F. Holmsen

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arXiv · 2408.05871

Helly type problems in convexity spaces

Andreas F. Holmsen

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Abstract

We report on some recent progress regarding combinatorial properties in convexity spaces with a bounded Radon number. In particular, we discuss the relationship between the Radon number, the colorful and fractional Helly properties, weak $\varepsilon$-nets, and $(p,q)$-theorems. As an application of the theory of convexity spaces we introduce new classes of uniform hypergraphs and show that they are $χ$-bounded.

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Andreas F. Holmsen. 2025-02-17. Helly type problems in convexity spaces. https://arxiv.org/abs/2408.05871

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